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Influences of Diffusion on Metabolic Structure and Function in Skeletal Muscle

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Influences of Diffusion on Metabolic Structure and Function in Skeletal Muscle 263 The Journal of Experimental Biology 214, 263-274 © 2011. Published by The Company of Biologists Ltd doi:10.1242/jeb.047985 Molecules in motion: influences of diffusion on metabolic structure and function in skeletal muscle Stephen T. Kinsey1,*, Bruce R. Locke2 and Richard M. Dillaman1 1Department of Biology and Marine Biology, University of North Carolina Wilmington, 601 South College Road, Wilmington, NC 28403-5915, USA and 2Department of Chemical and Biomedical Engineering, Florida State University, FAMU-FSU College of Engineering, 2525 Pottsdamer Street, Tallahassee, FL 32310, USA *Author for correspondence ([email protected]) Accepted 25 August 2010 Summary Metabolic processes are often represented as a group of metabolites that interact through enzymatic reactions, thus forming a network of linked biochemical pathways. Implicit in this view is that diffusion of metabolites to and from enzymes is very fast compared with reaction rates, and metabolic fluxes are therefore almost exclusively dictated by catalytic properties. However, diffusion may exert greater control over the rates of reactions through: (1) an increase in reaction rates; (2) an increase in diffusion distances; or (3) a decrease in the relevant diffusion coefficients. It is therefore not surprising that skeletal muscle fibers have long been the focus of reaction–diffusion analyses because they have high and variable rates of ATP turnover, long diffusion distances, and hindered metabolite diffusion due to an abundance of intracellular barriers. Examination of the diversity of skeletal muscle fiber designs found in animals provides insights into the role that diffusion plays in governing both rates of metabolic fluxes and cellular organization. Experimental measurements of metabolic fluxes, diffusion distances and diffusion coefficients, coupled with reaction–diffusion mathematical models in a range of muscle types has started to reveal some general principles guiding muscle structure and metabolic function. Foremost among these is that metabolic processes in muscles do, in fact, appear to be largely reaction controlled and are not greatly limited by diffusion. However, the influence of diffusion is apparent in patterns of fiber growth and metabolic organization that appear to result from selective pressure to maintain reaction control of metabolism in muscle. Key words: calcium, diffusion, metabolism, mitochondria, muscle, nuclei. Introduction in D values, diffusion distances and rates of reaction fluxes. For Physiologists have a long history of evaluating the role of diffusion instance, Ca2+ cycling entails a high D for Ca2+, short diffusion in cellular metabolism, particularly with respect to the necessity for distances and high reaction fluxes, whereas nuclear function entails O2 transport from the blood into cells for aerobic metabolism. low D values for various macromolecular products, long diffusion Indeed, Fick’s diffusion equations and principles of membrane distances and low reaction fluxes. These interactions mean that cell transport have a prominent position in most physiology textbooks, structure is responsive to diffusion constraints in a manner that is and biology students are well versed in the notion that cells are dependent on the type of process and the functional demands placed small in order to maintain short diffusion distances for molecules on that process. Fig.1 also illustrates the principle of facilitated like O2. A corollary of this rule in skeletal muscle is that aerobic diffusion that was first proposed for myoglobin (Mb) by Wittenberg fibers that rely on O2 diffusion to promote sustained exercise are (Wittenberg, 1959) and independently identified for hemoglobin generally smaller than anaerobic fibers that are used for burst (Hb) by Scholander (Scholander, 1960), but also applies to contraction and are less reliant on O2 diffusion (for review, see van phosphagen kinases such as creatine kinase (CK) and arginine Wessel et al., 2010). The implication of this observation is that kinase (AK), and to a lesser extent to parvalbumin (PA). In higher rates of aerobic metabolism require smaller fibers, and facilitated diffusion, protein binding or enzymatic conversion of the variation in fiber size may represent responses to avoid diffusion diffusing species provides a parallel pathway for diffusive flux that limitation. In a more general sense, we can conclude that in any enhances the overall rate of diffusive transport. The present paper reaction–diffusion system, the role of diffusion becomes greater as will attempt to summarize some of the ways in which diffusion the diffusion coefficient (D) decreases, diffusion distance increases governs metabolic structure and function in skeletal muscle. or the rate of reaction flux increases (Weisz, 1973). In principle, nearly every biochemical reaction is a Concentration gradients are a prerequisite for diffusion reaction–diffusion process involving the diffusive flux of substrates control of reaction flux to enzyme active sites. A number of processes have been the When examining a single tissue type, D is comparatively invariant subject of reaction–diffusion analyses in muscle, such as the over physiological time scales, so the extent to which diffusion aforementioned oxygen flux from capillaries to mitochondria influences cell structure and function is largely governed by the (Fig.1A), the diffusion of ATP to sites of cellular ATPases interaction between diffusion distance and reaction flux rate. In (Fig.1B), Ca2+ cycling during contraction–relaxation cycles skeletal muscle fibers rates of reaction fluxes and diffusion (Fig.1C), and the transport of nuclear products to sites of action in distances can vary over several orders of magnitude. For instance, the cell (Fig.1D). These examples illustrate considerable variation aerobic metabolic rate in white muscle from fishes and crustaceans THE JOURNAL OF EXPERIMENTAL BIOLOGY 264 S. T. Kinsey, B. R. Locke and R. M. Dillaman these approaches is that diffusion is rapid relative to the rate of metabolic flux, and it therefore does not limit reactions. A Fig.2 is a diagram of the manner in which diffusion distance and MbO MbO reaction flux interact to affect concentration profiles of a diffusing HbO2 2 2 Net diffusive molecule for cases where diffusion would not be limiting and for flux O O O cases where it may be limiting. In this example, there is a point +2 +2 +2 Hb Mb Mb source for the diffusing molecule and that molecule is consumed (sink) as it diffuses away from the source. For instance, the source 2H2O Capillary Muscle fiber could be a capillary supplying O2 that diffuses across the cell and B is consumed by mitochondria. The schematic diagram in Fig.2 ADP ADP illustrates that in cases where diffusion is fast relative to the +Pi AP/PCr AP/PCr +P reaction rate, there are no concentration gradients for the diffusing ½ O2 i AK/CK Net diffusive flux AK/CK ATPase species (red lines). This represents a situation where diffusion would have no effect on reaction rate, and an analysis of the H2O Arg/Cr Arg/Cr ATP ATP catalytic properties alone is sufficient to explain the metabolic Mitochondria process. Thus, an increase in the reaction rate or the diffusion distance (manifested here as increased activity or size, respectively, of the sink) would lead to a uniform reduction in the concentration C CsCa2+ PACa2+ PACa2+ TnCCa2+ ATP of the diffusing species over the diffusion distance. The blue lines Net diffusive flux illustrate what would be expected when diffusion is not much faster Ca2+ Ca2+ Ca2+ Ca2+ + + + + than the rate of reaction flux, leading to concentration gradients that Cs PA PA TnC become steeper as the reaction rate or the diffusion distance Sarcoplasmic increases. In these cases, if the diffusing species is a substrate for reticulum a reaction, then the rate of product formation may be reduced as the distance from the source increases. D Unfortunately, measurements of metabolite concentrations in cells typically cannot distinguish between the rapid diffusion and RNA, Net diffusive flux or Sites of proteins active transport action slow diffusion cases, as they do not give information on spatial variation in concentration. Most studies have therefore analyzed reaction–diffusion processes in muscle using mathematical models Nucleus that include independent measurements of D, diffusion distances and rates of reaction fluxes. This requires a clear understanding of Fig.1. Examples of reaction–diffusion processes in muscle. (A)O2 diffusion the nature of the intracellular environment and the manner in which entails reversible binding with hemoglobin (Hb) or another blood pigment small and large molecules move in this environment. type, and with myoglobin (Mb) in some fiber types. (B)Diffusion of ATP to cellular ATPases involves the reversible transfer of a phosphoryl group from ATP to an acceptor molecule such as creatine (Cr) or arginine (Arg), The intracellular environment of muscle has characteristics of forming the phosphagen phosphocreatine (PCr) or arginine phosphate a porous medium (AP), respectively. Phosphagen kinases, such as creatine kinase (CK) or The cytoplasm is a complex and crowded medium consisting of arginine kinase (AK) catalyze these reactions. (C)Ca2+ is released from the soluble and bound macromolecules, fibrous cytoskeletal elements sarcoplasmic reticulum (SR) upon muscle stimulation and must diffuse to and membrane-bound organelles (reviewed in Luby-Phelps, 2000; and bind myofibrillar troponin C (TnC) to activate
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